AAE-NA-Labs/Direct Methods for Solving Linear Systems/Alg8.m

34 lines
779 B
Matlab
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

function [L, U, P] = Alg8(A)
% LU Factorization with partial pivoting
% [L, U, P] = Alg8(A) decomposes matrix A using Crout's algorithm into
% U upper triangular matrix and L unit lower triangular matrix
% using partial pivoting, interchanging A's rows, such that AP = LU.
[m, n] = size(A);
L = zeros(m, n);
U = eye(m, n);
P = eye(m, n);
for k = 1:m
if A(k, k) == 0
non_zero_col = find(A(k, :), 1);
A(:, [k non_zero_col]) = deal(A(:, [non_zero_col k]));
P(:, [k non_zero_col]) = deal(P(:, [non_zero_col k]));
end
end
for k = 1:n
for j = k : n
U(k, j) = A(k, j) - dot(L(k, 1:k-1), U(1:k-1, j));
end
for i = k:n
L(i, k) = (A(i, k) - dot(L(i,1:k-1), U(1:k-1, k))) / U(k,k);
end
end
end